Scientific Computing
Science, Technology, Engineering, Arts & Math
Teaching & Learning Math & Science with Technology
Graphing Calculators, Numerical Methods, Computer Algebra Systems & Linux Clusters
Why Shadowfax? Our cluster is so fast that we named it after the Lord Of The Rings character!
Website once known as CalcPage.tripod.com (1988 – 2008)
Chapter 11 was all about Matrix Operations and Matrix Algebra. First we talked about solving 2D and 3D Linear Systems Of Equations using Augmented Matrices and Gauss-Jordan Elimination. Then we worked on Cramer's Rule With Determinants and we set up Matrix Equations to solve with Inverse Matrices! We even solved non-Linear 2D Systems and then we worked on Linear Programming a la John Nash's Min-Max Theorem!
UNIT08 was all about Advanced Integration Techniques with applications to Variable Separable Ordinary Differential Equations of 1st and 2nd Order including Exponential Growth and Decay, Newton's Law Of Heating and Cooling, Logistic Growth and Decay. We also talked about limits involving L'Hopital's Rule. We tried our hand at integrals involving ArcSin(x) and ArcTan(x). We integrated powers of sine and cosine. Then figured out Integration By Parts and Partial Fractions. We even tried Trig Sub! Last, but not least, we used Euler's Method and Slope Fields.
LAB06 was all about Iteration using for() and while() loops! We had fun applications making a multi-round game out of our Rock-Papper-Scissors game playing against the computer. We also played with Heron's Method and Newton's Method for finding roots and radicals numerically. We played around with convergence tables and limits. We even found tables of very large powers and Fibonacci sequence terms!
We successfully downloaded the latest pelicanHPC ISO (version 4.1 gnome), burned the ISO as a bootable DVD an booted the DVD in our lab. Now we can compile flops.f! flops.f is a program that stresses each core of your cluster scattering and gathering a Riemann Sum calculation for PI and calculating the cluster's performance. flops.f is written using openMPI and FORTRAN77:
mpif77 -o flops flops.f
Then we ran the flops executable:
mpirun -np 4 flops
mpirun -np 100 --hostfile machines flops
We can't set up a DHCP server to make a 100 core grid cluster anymore (second commandline) since IT made my room rejoin the WimpDoze DHCP server (after 24 years). BTW, machines is a text file listing all the DHCP allotted IP addresses on our intranet LAN.
So, we can run SMP Clusters (first commandline). In other words, we can use all 4 cores on our quadcore Lenovo PCs, but that's about it. Doing so, we achieved very good performance: 2GFLOP/s per core and 8GFLOP/s per Linux Box. Yes, I know, we don't have Linux Boxes anymore, but the pelicanHPC DVD boots up Debian Linux with a Gnome desktop, so we can dream, can't we?
Here's your January homework:
If you haven't done so already, download the pelicanHPC ISO file and burn your own bootable DVD. Don't worry if your first burn doesn't boot. You can use that DVD as a "Linux Coaster" for your favorite beverage the next time you play on SteamOS. If you can make this work at home, try to run Hello_World_MPI.py from John Burke's sample MPI4PY (MPI for Python) code. You can also try this tutorial.
Also, here's our third reading assignment. BTW, I was an editor on this book. That's why I recommend it. It's all about setting up and programming a Linux Cluster aka Super Computer with COWS (Commodity Off-the-shelf Work Stations = ordinary PCs). What's unique about this book is that it uses Java for all its coding samples making it an easy read for anyone who has taken AP CompSci!
You may also want to download and try out the BCCD ISO! I'm also looking at the hardware side of building our own cluster with RaspberryPi 3.0 single card computers which are also Debian and Python based. Maybe we'll play around with codrone to learn about programming drones too? Stay tuned!
NEW DECOR (Display Case):
Featuring ChromeCast & Processing!
NEW DECOR (Room 429):
Featuring Tapestry from RedBubble!
So, what's all this good for aside from making Fractal Zoom or Shrek Movies?
SETI Search
Econometrics
Bioinformatics
Protein Folding
Beal Conjecture
Scientific Computing
Computational Physics
Mersenne Prime Search
Computational Chemistry
Computational Astronomy
Computer Aided Design (CAD)
Computer Algebra Systems (CAS)
These are but a few examples of using Computer Science to solve problems in Mathematics and the Sciences (STEAM). In fact, many of these applications fall under the heading of Cluster Programming or Super Computing. These problems typically take too long to process on a single PC, so we need a lot more horse power. Next time, maybe we'll just use Titan!
Now that it's 2018, I suppose it's time for a New Year's Resolution: "I resolve not to get upset every time I see a blatant disregard for the proper use of units or a lack of number sense!" This problem shows up everywhere. I think you'd be very surprised by just how ubiquitous this issue really is! Take a look at just a few examples below:
Verizon To The Rescue!
This audio clip, turned YouTube video, is one of the most infamous examples of this complete disregard for number sense and dimensional analysis. Suffice it to say that an approximate 36000 KB cell phone data overage times 0.002 cents per KB is billed at approximately $72???
Potato Farmer
Me: My dear sir, that's quite a sign you have!
Farmer: Why, yes, we are having a big sale.
Me: I can see that! This sale is amazing!
Farmer: May I interest you in some potatoes?
Me: Certainly, I'll take 100lbs.
Farmer: Dear me, how wonderful...
Farmer: Just a minute while I fetch 100 bags!
Me: Thank you, take your time, no hurry...
Farmer: There you go, done loading your car.
Me: Here you are, my good man...
Me: You get a nice new crisp $1 bill...
Farmer: What's the meaning of this?
Me: You did such a fine job, keep the change!
Me: I know, it's way too generous,
Me: but I think you've earned it!
Farmer: This is an outrage!
Me: No, no, you can keep the change.
Me: After all, with the extra penny,
Me: you can get a whole pound for yourself
Me: with change to spare, no less!
(above: similar problem at my supermarket)
Library Matron
Clearly, the Librarian meant 10 cents per page printed from the PC Lab. However, under the unwritten rules of "Truth In Advertising" I would be fully within my rights to demand 10 printed pages for a single penny, no?
Local Deli
The Deli Guy is guilty of the same gross negligence of proper use of units aka dimensional analysis aka number sense! Did he mean 50 cents per sandwich? Shall we just give him a pass? No, say I, no more Mr Nice Guy! We can't let this slide anymore. Keep this up and it will soon be the end of civilization as we know it! How about 50 cents for 100 sandwiches?
Tile Store
Is the Tile clerk guilty of this mortal sin as well? So, shall we pay our 69 cents per tile and meekly walk away shaking our collective heads without uttering so much as a single cough in derision? No, I will make my order and pay 69 cents for 100 tiles! Maybe I'll take 1000 tiles off the clerk's hands for a measly $6.90! Why stop there, how about 10000.... OK, ok, now this is getting out of hand!
Parting Blow
Sorry, I have no further commentary. This last example just takes the cake!
Wait, just when you thought it could not get any worse, there's more:
OK, just one more:
This one opens up a whole other can of worms! My neighbor's mailbox is supposed to have a street address of 226 Such-And-Such Lane. Did he mix up his Roman Numerals with his Arabic Number System?
